On the matrix reorderings \(\Gamma\) and \(\Psi\) (Q1063086)

The authors discuss linear transformations of matrices which preserve the Hermitian or positive semidefinite matrices. A choice of basis in the space of matrices corresponds to a reordering of the entries. The authors exhibit the representations of linear transformations relative to several natural choices of bases and relate these to tensor and Kronecker products. The representations are used to infer spectral information for the two most frequently employed linear transformations.